Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
Relating path coverings to vertex labellings with a condition at distance two
Discrete Mathematics
On the $\lambda$-Number of $Q_n$ and Related Graphs
SIAM Journal on Discrete Mathematics
On the size of graphs labeled with condition at distance two
Journal of Graph Theory
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
On L(d, 1)-labelings of graphs
Discrete Mathematics
Labeling Products of Complete Graphs with a Condition at Distance Two
SIAM Journal on Discrete Mathematics
A Theorem about the Channel Assignment Problem
SIAM Journal on Discrete Mathematics
Circular Distance Two Labeling and the $\lambda$-Number for Outerplanar Graphs
SIAM Journal on Discrete Mathematics
Backbone colorings for graphs: Tree and path backbones
Journal of Graph Theory
Graph labeling and radio channel assignment
Journal of Graph Theory
Backbone Colorings and Generalized Mycielski Graphs
SIAM Journal on Discrete Mathematics
L(2,1)-labelings of Cartesian products of two cycles
Discrete Applied Mathematics
Backbone colorings of graphs with bounded degree
Discrete Applied Mathematics
Hi-index | 0.04 |
Suppose that G is a graph and that H is a subgraph of G. Let L be a mapping that assigns to each vertex v of G a set L(v) of positive integers. We say that (G,H) is backboneL-colourable if there is a proper vertex colouring c of G such that c(v)@?L(v) for all v@?V, and |c(u)-c(v)|=2 for every edge uv in H. We say that (G,H) is backbone k-choosable if (G,H) is backbone L-colourable for any list assignment L with |L(v)|=k for all v@?V(G). The backbone choice number of (G,H), denoted by ch"B"B(G,H), is the minimum k such that (G,H) is backbone k-choosable. The concept of a backbone choice number is a generalization of both the choice number and the L(2,1)-choice number. Precisely, if E(H)=0@?, then ch"B"B(G,H)=ch(G), where ch(G) is the choice number of G; if G=H^2, then ch"B"B(G,H) is the same as the L(2,1)-choice number of H. In this article, we first show that, if |L(v)|=d"G(v)+2d"H(v), then (G,H) is L-colourable, unless E(H)=0@? and each block of G is a complete graph or an odd cycle. This generalizes a result of Erdos, Rubin, and Taylor on degree-choosable graphs. Second, we prove that ch"B"B(G,H)=